Fluid streams having time-variant properties are generated in many processes which operate in cyclic or discontinuous modes. The time variance of certain stream properties can adversely affect the use of the stream elsewhere in the process or in other applications. For example, in the recovery of hydrogen from synthesis gas by pressure swing adsorption, blowdown and purge streams are generated in which the concentrations of combustible components vary periodically with time. These byproduct streams typically are used as fuel to fire a process furnace, and the performance of the furnace can be adversely affected by the resulting time-variant heating value of the fuel stream. Other examples can be found in cyclic or discontinuous processes such as the smelting of ore in the primary metals industries, operation of batch chemical reactors or the venting of process upsets to buffer tanks in the chemical process industries, and variations in wastewater composition in wastewater treatment processes.
Typical time-variant stream properties are temperature, pH, and the concentrations of particular components in the stream. The amplitude of the time variance of the properties of such streams can be reduced or attenuated by two well-known methods.
In one method, something is added to or removed from the stream in a controlled manner to compensate for the variations. For example, heat can be added to or removed from a stream to control temperature or another stream can be added under controlled conditions to the time-variant stream, such as the addition of acid or alkali to control the pH of a stream. This method often is used when the time variance of a desired property is largely random in nature.
In the other method, the time-variant stream is introduced into a holding volume such that the natural capacitance of the volume reduces or attenuates the amplitude of the time variance of the outlet stream properties relative to the inlet stream properties. Nothing is added to or removed from the stream. Mixing of the fluid in the holding volume promotes a constant composition throughout the volume and improves the reduction of the time variance of the outlet stream relative to the inlet stream. This method often is used when the time variance of a desired property is primarily periodic in nature. Mixing can be effected by mechanical agitation, by inlet distributors or jets which utilize pressure drop to promote mixing, or by baffles which promote turbulence.
The appropriate use of liquid or gaseous byproduct streams can have a significant positive impact on the capital and operating costs of a process plant. When these byproduct streams have time-variant properties, mixing of some kind usually is required to reduce the time-variant properties before these byproduct streams are used in the process. Improved mixing methods thus are desirable to reduce initial plant investment and ongoing plant operating cost. The invention disclosed below and defined by the claims which follow offers a new method for attenuating the amplitude of time-variant properties of a fluid stream by controlled mixing in an enclosed volume.
In one embodiment, the invention is a method for attenuating the amplitude of a time-variant property of a fluid stream which comprises introducing into an enclosed volume an inlet fluid stream having a time-variant property, dividing the fluid within the enclosed volume into portions of fluid having different residence times therein, combining the portions of fluid, and withdrawing from the enclosed volume an outlet fluid stream having an attenuated time-variant property such that the residence time distribution of the outlet fluid stream is characterized by a flatness constraint Fxcex8 equal to or less than about 0.11 and a symmetry constraint Sxcex8 equal or less than about 0.075, wherein the flatness constraint Fxcex8 is defined as       F    θ    =                    ∫        0        2            ⁢                                    [                          0.5              -                                                E                  θ                                ⁢                                  (                  θ                  )                                                      ]                    2                ⁢                  xe2x80x83                ⁢                  ⅆ          θ                      +                  ∫        2        ∞            ⁢                                    [                                          E                θ                            ⁢                              (                θ                )                                      ]                    2                ⁢                  xe2x80x83                ⁢                  ⅆ          θ                    
and the symmetry constraint Sxcex8 is defined as       S    θ    =                    ∫        0        1            ⁢                                    [                                                            E                  θ                                ⁢                                  (                  θ                  )                                            -                                                E                  θ                                ⁢                                  (                                      2                    -                    θ                                    )                                                      ]                    2                ⁢                  xe2x80x83                ⁢                  ⅆ          θ                      +                  ∫        2        ∞            ⁢                                    [                                          E                θ                            ⁢                              (                θ                )                                      ]                    2                ⁢                  xe2x80x83                ⁢                  ⅆ          θ                    
where the function Excex8 (xcex8) is the overall dimensionless residence time distribution of the outlet fluid stream and xcex8 is the dimensionless time.
The time-variant property of the fluid stream can vary randomly with time or alternatively can vary periodically with time. When the time-variant property of the fluid stream varies periodically with time, the enclosed volume can comprise a mixing zone and piping for dividing the inlet fluid stream into multiple fluid streams which are introduced into the mixing zone at multiple locations. The fluid in the mixing zone has a mean residence time defined as the volume of the mixing zone divided by the actual volumetric flow rate of the inlet fluid stream, and wherein this mean residence time is between about 0.3 and about 0.7 times the period of a cyclic time-variant property of the inlet fluid stream. The enclosed volume can include a mixing zone and piping for withdrawing fluid from the mixing vessel at multiple locations.
The fluid withdrawn from the mixing zone at multiple locations can be combined into an outlet fluid stream, wherein the mixing zone has a mean residence time defined as the volume of the mixing zone divided by the actual volumetric flow rate of the inlet fluid stream and wherein this mean residence time is between about 0.3 and about 0.7 times the period of a cyclic time-variant property of the inlet fluid stream.
The time-variant property of the inlet fluid stream can be selected from the group consisting of temperature, the concentration of a component in the stream, pH, thermal conductivity, electrical conductivity, viscosity, molecular weight, heat capacity, lower heating value, and higher heating value.
The inlet fluid stream can be a multicomponent gas mixture comprising hydrogen, methane and carbon dioxide, and the time-variant property of the inlet fluid stream can be the concentration of methane therein. This inlet fluid stream can comprise blowdown gas and purge effluent gas from a pressure swing adsorption process for removing at least methane and carbon dioxide from a mixture comprising at least hydrogen, methane, and carbon dioxide.
In another embodiment, the invention is a method for attenuating the amplitude of a time-variant property of a fluid stream which comprises dividing an inlet fluid stream having a time-variant property into three or more individual fluid streams, introducing each of the individual fluid streams into a mixing zone at a different entrance location in the zone, and withdrawing from an outlet location of the mixing zone an outlet fluid stream having a time-variant property amplitude which is attenuated relative to the amplitude of the time-variant property of the inlet fluid stream, wherein (1) at least first, second, and third individual fluid streams are withdrawn successively from the inlet fluid stream and introduced successively into the mixing zone at first, second, and third entrance locations, respectively, wherein the distances from the outlet location to the first, second, and third entrance locations increase respectively, and wherein the distance between the second and third entrance locations is less than the distance between the first and second entrance locations or (2) the flow rate of one of the individual fluid streams is different than the flow rate of another of the individual fluid streams, or (3) the flow rate of one of the individual fluid streams is different than the flow rate of another of the individual fluid streams and at least first, second, and third individual fluid streams are withdrawn successively from the inlet fluid stream and introduced successively into the mixing zone at first, second, and third entrance locations, respectively, wherein the distances from the outlet location to the first, second, and third entrance locations is less than the distance between the first and second entrance locations.
Another embodiment of the invention relates to a method for attenuating the amplitude of a time-varient property of a fluid stream which comprises
(a) dividing an inlet fluid stream having a time-variant property into three or more individual fluid streams, introducing each of the individual fluid streams into a mixing zone at a different entrance location in the zone, and withdrawing from the mixing zone an outlet fluid stream having a time-varient property amplitude which is attenuated relative to the amplitude of the time-varient property of the inlet fluid stream, wherein (1) the distance between at least one pair of adjacent entrance locations is different than the distance between another pair of adjacent entrance locations, or (2) the flow rate of one of the individual fluid streams is different than the flow rate of another of the individual fluid streams, or (3) the distance between at least one pair of adjacent entrance locations if different than the distance between another pair of adjacent entrance locations and the flow rate of one of the individual fluid streams is different than the flow rate of another of the individual fluid streams; and
(b) attenuating the amplitude of a time-variant property of the outlet fluid stream by dividing the outlet fluid stream into three or more additional individual fluid streams, introducing each of the additional individual fluid streams into an additional mixing zone at a different respective entrance location in the zone, and withdrawing from the additional mixing zone a second outlet fluid stream having a time-variant property of which the amplitude is further attenuated relative to the amplitude of the time-variant property of the outlet fluid stream, wherein in the additional mixing vessel (1) the distance between at least one pair of adjacent entrance locations is different than the distance between another pair of adjacent entrance locations, or (2) the flow rate of one of the individual fluid portions is different than the flow rate of another of the individual fluid portions, or (3) the distance between at least one pair of adjacent entrance locations is different than the distance between another pair of adjacent entrance locations and the flow rate of one of the individual fluid portions is different than the flow rate of another of the individual fluid portions.
Another variation of this embodiment can further comprise withdrawing one or more additional outlet fluid streams from the mixing zone, wherein the outlet fluid stream and the additional outlet fluid streams are withdrawn at different exit locations in the mixing zone, wherein (1) the distance between at least one pair of adjacent exit locations is different than the distance between another pair of adjacent exit locations, or (2) the flow rate of one of the outlet fluid streams is different than the flow rate of another of the outlet fluid streams, or (3) the distance between at least one pair of adjacent exit locations is different than the distance between another pair of adjacent exit locations and the flow rate of one of the outlet fluid streams is different than the flow rate of another of the outlet fluid streams.
In yet another embodiment, the invention is a method for attenuating the amplitude of a time-variant property of a fluid stream which comprises introducing into an inlet location in a mixing zone an inlet fluid stream having a time-variant property, withdrawing three or more individual fluid portions at different exit locations in the mixing zone, and combining the three or more individual fluid portions into a combined exit fluid stream having a time-variant property of which the amplitude is attenuated relative to the amplitude of the time-variant property of the inlet fluid stream, wherein (1) the distances between pairs of adjacent exit locations decrease as the distance between each adjacent exit location and the inlet location increase, or (2) the flow rate of one of the individual fluid portions is different than the flow rate of another of the individual fluid portions, or (3) the distances between pairs of adjacent exit locations decrease as the distances between each adjacent exit location and the inlet location increase and the flow rate of one of the individual fluid portions is different than the flow rate of another of the individual fluid portions.
Another embodiment of the invention relates to a method for attenuating the amplitude of a time-varient property of a fluid stream which comprises
(a) introducing an inlet fluid stream having a time-variant property into a mixing zone, withdrawing three or more individual fluid portions at different exit locations in the mixing zone, and combining the three or more individual fluid portions into a combined exit fluid stream having a time-varient property of which the amplitude is attenuated relative to the amplitude of the time-variant property of the inlet fluid stream, wherein (1) the distance between at least one pair of adjacent exit locations is different than the distance between another pair of adjacent exit locations, or (2) the flow rate of one of the individual fluid portions is different than the flow rate of another of the individual fluid or portions, (3) the distance between at least one pair of adjacent exit locations is different than the distance between another pair of adjacent exit locations and the flow rate of one of the individual fluid portions is different than the flow rate of another of the individual fluid portions; and
(b) introducing the combined exit fluid stream into an additional mixing zone, withdrawing three or more individual fluid portions at different exit locations in the mixing zone, and combining the three or more individual fluid portions into another combined exit fluid stream having a time-variant property of which the amplitude is attenuated relative to the amplitude of a time-variant property of the combined exit fluid stream, wherein (1) the distance between at least one pair of adjacent exit locations is different than the distance between another pair of adjacent exit locations, or (2) the flow rate of one of the individual fluid portions is different than the flow rate of another of the individual fluid portions, or (3) the distance between at least one pair of adjacent exit locations is different than the distance between another pair of adjacent exit locations and the flow rate of one of the individual fluid portions is different than the flow rate of another of the individual fluid portions.
In a further embodiment, the invention is a method for attenuating the amplitude of a time-variant property of a fluid which comprises introducing into a mixing zone two or more inlet fluid streams through two or more inlets and withdrawing two or more outlet fluid streams from the mixing zone through two or more outlets, with the provisos that (1) the number of inlet fluid streams and the number of outlet fluid streams cannot both equal one, and (2) the number of inlet fluid streams is at least three, or the number of outlet fluid streams is at least three, or the number of inlet fluid streams is at least three and the number of outlet fluid streams is at least three; wherein (a) the flow rate of one of the inlet fluid streams is different than the flow rate of another of the inlet fluid streams, or (b) the flow rate of one of the outlet fluid streams is different than the flow rate of another of the outlet fluid streams, or (c) the flow rate of one of the inlet fluid streams is different than the flow rate of another of the inlet fluid streams and the flow rate of one of the outlet fluid streams is different than the flow rate of another of the outlet fluid streams.
The invention also includes an apparatus for attenuating the amplitude of a time-variant property of a fluid stream which comprises an enclosed volume, wherein the enclosed volume includes
(a) a mixing zone having three or more inlets and an outlet;
(b) piping means for dividing an inlet fluid stream into three or more individual fluid streams;
(c) piping means for introducing the three or more individual fluid streams respectively into the three or more inlets, and
(d) piping means for withdrawing an outlet fluid stream from the outlet of the mixing zone;
wherein the distance between at least one pair of adjacent inlets is different than the distance between another pair of adjacent inlets.
This apparatus can further comprise piping means for withdrawing a portion of the fluid from the piping means of (b) and introducing it into the piping means of (d). In this apparatus, the mixing zone can be a mixing vessel characterized by an axis wherein the axial distance Dn from any inlet to the outlet is defined by       D    n    =            (              d        /        N            )        ⁢                  ∑                  i          =          0                          n          -          1                    ⁢              xe2x80x83            ⁢              (                  N          -          i                )            
where n is an integer with a value of 1 through N, integers 1 through N denote sequential inlets, N is the total number of inlets to the mixing vessel, the inlet denoted by n =1 is the inlet nearest the outlet, the inlet denoted by n=N is the inlet farthest from the outlet, and d is the axial distance between the outlet and the inlet nearest the outlet.
This apparatus can further comprise another inlet located between the inlet denoted by n =1 and the outlet. The mixing vessel can be a cylinder with the outlet at either end of the cylinder, and the inlets can be arranged in a line parallel to the axis of the cylinder. The inlets can comprise openings of essentially the same cross sectional area, or alternatively can comprise openings of different cross sectional areas.
The invention includes another apparatus for attenuating the amplitude of a time-variant property of a fluid stream, which apparatus can comprise an enclosed volume, wherein the enclosed volume includes
(a) a mixing zone having an inlet and three or more outlets;
(b) piping means for introducing an inlet fluid stream into the inlet of the mixing zone; and
(c) piping means for withdrawing from the mixing zone three or more individual fluid portions through the three or more outlets and combining the three or more individual fluid portions into an outlet fluid stream;
wherein the distance between at least one pair of adjacent outlets is different than the distance between another pair of adjacent outlets.
This apparatus can further comprise piping means for withdrawing a portion of the fluid from the piping means of (b) and introducing it into the outlet fluid stream in the piping means of (c). The mixing zone can comprise a cylindrical volume which is characterized by an axis, wherein the axial distance Dn from the inlet means to any outlet is defined by       D    n    =            (              d        /        N            )        ⁢                  ∑                  i          =          0                          n          -          1                    ⁢              xe2x80x83            ⁢              (                  N          -          i                )            
where n is an integer with a value of 1 through N, integers 1 through N denote sequential outlets, N is the total number of outlets from the mixing zone, the outlet denoted by n=1 is the outlet nearest the inlet, the outlet denoted by n=N is the outlet farthest from the inlet, and d is the axial distance between the inlet and the outlet nearest the inlet.
In this apparatus, the piping means of (c) can include means for withdrawing another individual fluid portion at a location between the outlet denoted by n=1 and the inlet means of (b). The mixing zone can comprise a cylindrical volume with the inlet means at either end of the cylindrical volume and the outlets arranged in a line parallel to the axis of the cylindrical volume. The outlets can comprise openings of essentially the same cross sectional area, or alternatively can comprise openings of different cross sectional areas.
The invention includes another apparatus for attenuating the amplitude of a time-variant property of a fluid, which apparatus can comprise an enclosed volume, wherein the enclosed volume includes
(a) a mixing zone having one or more inlets and one or more outlets, with the provisos that (1) the number of inlets and the number of outlets cannot both equal one, and (2) the number of inlets is at least three, or the number of outlets is at least three, or the number of inlets is at least three and the number of outlets is at least three;
(b) piping means for conducting the fluid to the one or more inlets of the mixing zone;
(c) piping means for withdrawing fluid from the mixing zone through the one or more outlets and providing an outlet fluid stream;
wherein (1) the distance between at least one pair of adjacent inlets is different than the distance between another pair of adjacent inlets, (2) the distance between at least one pair of adjacent outlets is different than the distance between another pair of adjacent outlets, or (3) the distance between at least one pair of adjacent inlets is different than the distance between another pair of adjacent inlets and the distance between at least one pair of adjacent outlets is different than the distance between another pair of adjacent outlets.
Another embodiment of the invention includes a method for attenuating the amplitude of a time-variant property of a fluid stream which comprises dividing an inlet fluid stream having a time-variant property into three or more individual fluid streams, introducing each of the individual fluid streams into a mixing zone at a different entrance location in the zone, and withdrawing from the mixing zone an outlet fluid stream having a time-variant property amplitude which is attenuated relative to the amplitude of the time-variant property of the inlet fluid stream, wherein
(a) the distance between at least one pair of adjacent entrance locations is different than the distance between another pair of adjacent entrance locations; or the flow rate of one of the individual fluid streams is different than the flow rate of another of the individual fluid streams; or the distance between at least one pair of adjacent entrance locations is different than the distance between another pair of adjacent entrance locations and the flow rate of one of the individual fluid streams is different than the flow rate of another of the individual fluid streams; and
(b) the residence time distribution of the outlet fluid stream is characterized by a flatness constant Fxcex8 equal to or less than about 0.11 and a symmetry constraint Sxcex8 equal or less than about 0.075, wherein the flatness constraint Fxcex8 is defined as       F    θ    =                    ∫        0        2            ⁢                                    [                          0.5              -                                                E                  θ                                ⁢                                  (                  θ                  )                                                      ]                    2                ⁢                  xe2x80x83                ⁢                  ⅆ          θ                      +                  ∫        2        ∞            ⁢                                    [                                          E                θ                            ⁢                              (                θ                )                                      ]                    2                ⁢                  xe2x80x83                ⁢                  ⅆ          θ                    
and the symmetry constraint Sxcex8 is defined as       S    θ    =                    ∫        0        1            ⁢                                    [                                                            E                  θ                                ⁢                                  (                  θ                  )                                            -                                                E                  θ                                ⁢                                  (                                      2                    -                    θ                                    )                                                      ]                    2                ⁢                  xe2x80x83                ⁢                  ⅆ          θ                      +                  ∫        2        ∞            ⁢                                    [                                          E                θ                            ⁢                              (                θ                )                                      ]                    2                ⁢                  xe2x80x83                ⁢                  ⅆ          θ                    
where the function Excex8 (xcex8) is the overall dimensionless residence time distribution of the outlet fluid stream and xcex8 is the dimensionless time.
An alternative embodiment of the invention relates to a method for attenuating the amplitude of a time-variant property of a fluid stream which comprises introducing an inlet fluid stream having a time-variant property into a mixing zone, withdrawing three or more individual fluid portions at different exit locations in the mixing zone, and combining the three or more individual fluid portions into a combined exit fluid stream having a time-variant property of which the amplitude is attenuated relative to the amplitude of the time-variant property of the inlet fluid stream, wherein
(a) the distance between at least one pair of adjacent exit locations is different than the distance between another pair of adjacent exit locations; or the flow rate of one of the individual fluid portions is different than the flow rate of another of the individual fluid portions; or the distance between at least one pair of adjacent exit locations is different than the distance between another pair of adjacent exit locations and the flow rate of one of the individual fluid portions is different than the flow rate of another of the individual fluid portions; and
(b) the residence time distribution of the outlet fluid stream is characterized by a flatness constraint Fxcex8 equal to or less than about 0.11 and a symmetry constraint Sxcex8 equal or less than about 0.075, wherein the flatness constraint Fxcex8 is defined as       F    θ    =                    ∫        0        2            ⁢                                    [                          0.5              -                                                E                  θ                                ⁢                                  (                  θ                  )                                                      ]                    2                ⁢                  xe2x80x83                ⁢                  ⅆ          θ                      +                  ∫        2        ∞            ⁢                                    [                                          E                θ                            ⁢                              (                θ                )                                      ]                    2                ⁢                  xe2x80x83                ⁢                  ⅆ          θ                    
and the symmetry constraint Sxcex8 is defined as       S    θ    =                    ∫        0        1            ⁢                                    [                                                            E                  θ                                ⁢                                  (                  θ                  )                                            -                                                E                  θ                                ⁢                                  (                                      2                    -                    θ                                    )                                                      ]                    2                ⁢                  xe2x80x83                ⁢                  ⅆ          θ                      +                  ∫        2        ∞            ⁢                                    [                                          E                θ                            ⁢                              (                θ                )                                      ]                    2                ⁢                  xe2x80x83                ⁢                  ⅆ          θ                    
where the function Excex8 (xcex8) is the overall dimensionless residence time distribution of the outlet fluid stream and xcex8 is the dimensionless time.